Consider a Glosten-Milgrom model in which the true value of a security is either 360p or 280p. In the market, 30% of traders are informed traders. Uninformed traders are equally likely to buy or sell the security, irrespective of its true value. The ask price quoted by the market maker for the first trade is 340p. Draw a well-labelled ‘decision tree’ style diagram showing the possible alternative trading scenarios for the first trade; and deduce what bid price the market maker should quote.
Suppose the first trade is a sell. Deduce what bid and ask prices the market maker should quote for the second trade; and discuss in brief the changes in bid price, ask price and spread.